AbstractFor a tree T of order n, let Ω(T)={X∈Ωn∣X⩽A(T)+In}, where Ωn denotes the set of all doubly stochastic matrices of order n and A(T) denotes the adjacency matrix of T, and let μ(T) denote the minimum permanent of matrices in Ω(T). Let Pn denote the path of length n−1 and K1,n−1 the complete bipartite graph on 1+(n−1) vertices. In this paper, it is shown that Pn and K1,n−1 are the only trees with minimal and maximal μ-values respectively among all trees of order n
For a fixed tree T with n vertices the corresponding acyclic Birkhoff polytope Ωn(T)consists of doub...
AbstractLet Pn denote the n×n permutation matrix with 1's in the positions (i,j) where j ≡ i + 1 (mo...
AbstractA conjecture on the permanents of doubly stochastic matrices is proposed. Some results suppo...
AbstractFor positive integers r, n with n⩾r+1, letDr,n=OrJJIn,where Js denote the matrices of 1s of ...
AbstractIn this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly sto...
AbstractWe determine the minimum permanents and minimizing matrices on the faces of Ωn+2 for the ful...
AbstractWe consider the minimum value of the permanent over certain faces of ωn, the polytope of n ×...
AbstractA sharp lower bound for the smallest entries, among those corresponding to edges, of doubly ...
AbstractWe consider the minimum permanents and minimising matrices on the faces of the polytope of d...
AbstractFor n ⩾ 6, we determine the minimum permanents and minimizing matrices on the faces of Ω3 + ...
AbstractIt is shown that the set Ωn(Zk) of n × n doubly stochastic matrices with prescribed zeros in...
AbstractWe determine the minimum permanent on generalized Hessenberg faces of the polytope of doubly...
AbstractFor a tree T of order n, let Ω(T)={X∈Ωn∣X⩽A(T)+In}, where Ωn denotes the set of all doubly s...
AbstractIt is shown that for each n ⩾ 7 there exists an n × n, irreducible, doubly stochastic matrix...
AbstractWe determine the minimum permanents and minimizing matrices over certain faces of the polyto...
For a fixed tree T with n vertices the corresponding acyclic Birkhoff polytope Ωn(T)consists of doub...
AbstractLet Pn denote the n×n permutation matrix with 1's in the positions (i,j) where j ≡ i + 1 (mo...
AbstractA conjecture on the permanents of doubly stochastic matrices is proposed. Some results suppo...
AbstractFor positive integers r, n with n⩾r+1, letDr,n=OrJJIn,where Js denote the matrices of 1s of ...
AbstractIn this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly sto...
AbstractWe determine the minimum permanents and minimizing matrices on the faces of Ωn+2 for the ful...
AbstractWe consider the minimum value of the permanent over certain faces of ωn, the polytope of n ×...
AbstractA sharp lower bound for the smallest entries, among those corresponding to edges, of doubly ...
AbstractWe consider the minimum permanents and minimising matrices on the faces of the polytope of d...
AbstractFor n ⩾ 6, we determine the minimum permanents and minimizing matrices on the faces of Ω3 + ...
AbstractIt is shown that the set Ωn(Zk) of n × n doubly stochastic matrices with prescribed zeros in...
AbstractWe determine the minimum permanent on generalized Hessenberg faces of the polytope of doubly...
AbstractFor a tree T of order n, let Ω(T)={X∈Ωn∣X⩽A(T)+In}, where Ωn denotes the set of all doubly s...
AbstractIt is shown that for each n ⩾ 7 there exists an n × n, irreducible, doubly stochastic matrix...
AbstractWe determine the minimum permanents and minimizing matrices over certain faces of the polyto...
For a fixed tree T with n vertices the corresponding acyclic Birkhoff polytope Ωn(T)consists of doub...
AbstractLet Pn denote the n×n permutation matrix with 1's in the positions (i,j) where j ≡ i + 1 (mo...
AbstractA conjecture on the permanents of doubly stochastic matrices is proposed. Some results suppo...
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